Factor. \[ v^{3}+27 \] \( v^{3}+27=\square \) (Factor completely.)

To factor \( v^3 + 27 \), you can recognize that it is a sum of cubes, which can be expressed in the form \( a^3 + b^3 \). Here, \( a = v \) and \( b = 3 \) because \( 27 = 3^3 \). The formula for the sum of cubes is: \[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \] Applying this to your expression: \[ v^3 + 27 = (v + 3)(v^2 - 3v + 9) \] Now, you have \( v^3 + 27 = (v + 3)(v^2 - 3v + 9) \), which factors the expression completely. Happy factoring! To ensure you have the right factorization, you might want to expand \( (v + 3)(v^2 - 3v + 9) \) back out and check if you get \( v^3 + 27 \) again. It's a good habit to verify your answers!